Method for encoding based on parity check matrix of LDPC code in wireless communication system and terminal using this

ABSTRACT

A method for performing encoding on the basis of a parity check matrix of a low density parity check code according to the present embodiment comprises the steps of: generating a parity check matrix by a terminal, wherein the parity check matrix corresponds to a characteristic matrix, each component of the characteristic matrix corresponds to a shift index value determined through a modulo operation between a corresponding component in a basic matrix and Zc, which is a lifting value, and the basic matrix is a 42×52 matrix; and performing encoding of input data, by the terminal, using the parity check matrix, wherein the lifting value is associated with the length of the input data.

TECHNICAL FIELD

The present disclosure relates to wireless communication and, moreparticularly, to a method of performing encoding based on a parity checkmatrix of an LDPC code in a wireless communication system and a userequipment using the same.

BACKGROUND ART

A conventional low-density parity-check (LDPC) encoding method has beenused in wireless communication systems such as an IEEE 802.11n wirelesslocal area network (WLAN) system, an IEEE 802.16e mobile WiMAX system,and a DVB-S2 system. The LDPC encoding method is basically a type oflinear block code and, therefore, operation of the LDPC encoding methodis performed by multiplication of a parity check matrix by an inputvector.

It is predicted that data transmission for fifth generation (5G)communication will support from a maximum of 20 Gbps to a minimum of afew tens of bps (e.g., 40 bits in the case of LTE). In other words, tosupport wide coverage of data transmission, it is necessary to supportvarious code rates. To meet such a requirement, various encoding methodsbased on an LDPC code are under discussion.

DETAILED DESCRIPTION OF THE INVENTION Technical Problems

An object of the present disclosure is to provide a method of performingencoding and a user equipment using the same, based on a parity checkmatrix of an LDPC code which is favorable in terms of latency intransmission of a short block with a relatively short length.

Technical Solutions

According to an aspect of the present disclosure, provided herein is amethod of performing encoding based on a parity check matrix of alow-density parity-check (LDPC) code, including generating the paritycheck matrix by a user equipment, wherein the parity check matrixcorresponds to a characteristic matrix, each element of thecharacteristic matrix corresponds to a shift index value determined by amodulo operation between a corresponding element in a base matrix and alifting value Zc, and the base matrix is a 42×52 matrix; and performingencoding on input data using the parity check matrix by the userequipment, wherein the lifting value is associated with the length ofthe input data.

Advantageous Effects

According to an embodiment of the present disclosure, there are provideda method of performing encoding and a user equipment using the same,based on a parity check matrix of an LDPC code which is favorable interms of latency in transmission of a short block with a relativelyshort length.

DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of a wireless communication system accordingto an embodiment of the present disclosure.

FIG. 2 is a diagram referenced to explain characteristics of a submatrixP.

FIG. 3 is a diagram illustrating a parity check matrix according to anembodiment of the present disclosure.

FIG. 4 is a diagram illustrating a characteristic matrix correspondingto a parity check matrix according to an embodiment of the presentdisclosure.

FIG. 5 is a diagram illustrating the structure of a base matrix for aparity check matrix according to an embodiment of the presentdisclosure.

FIG. 6 illustrates a matrix A belonging to a base matrix according to anembodiment of the present disclosure.

FIGS. 7A and 7B illustrate a matrix C belonging to a base matrixaccording to an embodiment of the present disclosure.

FIGS. 8A and 8B illustrate a matrix C belonging to a base matrixaccording to an embodiment of the present disclosure.

FIG. 9 is a flowchart illustrating a method of performing encoding basedon a parity check matrix of an LDPC code according to an embodiment ofthe present disclosure.

FIG. 10 is a flowchart illustrating a method of performing a decodingprocedure for a transport block based on any one of parity checkmatrices of two types according to another embodiment of the presentdisclosure.

FIG. 11 is a flowchart illustrating a method of performing code blocksegmentation based on a parity check matrix of an LDPC accord to anotherembodiment of the present disclosure.

FIG. 12 is a flowchart illustrating a method of performing a decodingprocedure based on a parity check matrix according to another embodimentof the present disclosure.

BEST MODE FOR CARRYING OUT THE INVENTION

The above-described characteristics and the following detaileddescription are merely exemplary details that are given to facilitatethe description and understanding of this disclosure. More specifically,this disclosure may be implemented in another format without beingrestricted only to the exemplary embodiment presented herein. Thefollowing exemplary embodiments are merely examples that are given tofully disclose this disclosure and to describe this disclosure to anyoneskilled in the technical field to which this disclosure pertains.Accordingly, if plural methods for implementing the elements of thepresent disclosure exist, it should be clarified that this disclosurecan be implemented by any one specific or similar method.

In this disclosure, if a structure is described as including specificelements, or if a procedure is described as including specific processsteps, this indicates that other elements or other process steps may befurther included. More specifically, it will be apparent that the termsused in this disclosure are merely given to describe a specificexemplary embodiment of the present disclosure and that such terms willnot be used to limit the concept or idea of this disclosure.Furthermore, it will also be apparent that the examples given tofacilitate the understanding of the invention also include complementaryembodiments of the given examples.

Each of the terms used in this disclosure is given a meaning that can begenerally understood by anyone skilled in the technical field to whichthis disclosure pertains. Each of the terms that are generally usedherein should be understood and interpreted by its uniform meaning inaccordance with the context of this disclosure. Moreover, the terms usedin this disclosure should not be interpreted as excessively ideal orformal meaning unless otherwise defined clearly. The appended drawingsare given to describe the exemplary embodiment of this disclosure.

FIG. 1 is a block diagram of a wireless communication system accordingto an embodiment of the present disclosure.

Referring to FIG. 1, the wireless communication system may include atransmission user equipment (UE) 10 and a reception UE 20.

The transmission UE 10 may include an LDPC encoder 100 and a modulator200. The LDPC encoder 100 may receive data m, encode the received datam, and output a codeword c. The modulator 200 may receive the codeword cand perform radio modulation on the received codeword c. The radiomodulated codeword may be transmitted to the reception UE 20 through anantenna.

It may be appreciated that a processor (not shown) of the transmissionUE 10 includes the LDPC encoder 100 and the modulator 200 and isconnected to the antenna of the transmission UE 10.

The reception UE 20 may include a demodulator 300 and an LDPC decoder400. The demodulator 300 may receive the radio modulated codewordthrough an antenna and demodulate the radio modulated codeword into thecodeword c. The LDPC decoder 400 may receive the codeword c, decode thecodeword c, and output the data m.

It may be appreciated that a processor (not shown) of the reception UE20 includes the demodulator 300 and the LDPC decoder 400 and isconnected to the antenna of the reception UE 20.

In other words, the wireless communication system of FIG. 1 may encodethe data m into the codeword c using the LDPC encoder 100 and decode thecodeword c into the data m using the LDPC decoder 400.

Thereby, the data may be stably transmitted and received between thetransmission UE 10 and the reception UE 20. An LDPC encoding method anddecoding method according to the present embodiment may be performedbased on a parity check matrix H.

In the present disclosure, the data m may be referred to as input data.The parity check matrix H may represent a matrix for checking whether anerror is included in the codeword c received by the LDPC decoder 400.The parity check matrix H may be prestored in a memory (not shown) ofeach of the transmission UE 10 and the reception UE 20.

Hereinafter, embodiments of the present disclosure will be described onthe premise that a quasi-cyclic LDPC code is applied. The parity checkmatrix H may include a plurality of submatrices P. Each submatrix P maybe a zero matrix O, or a circulant matrix acquired by shifting anidentity matrix I.

To encode data from a general linear block code, a generate matrix G isneeded. According to the above assumption, since the present embodimentis based on a quasi-cyclic LDPC method, the LDPC encoder 100 may encodethe data m into the codeword c using the parity check matrix H withoutan additional generate matrix G.

The LDPC encoder 100 may encode the data m into the codeword c using theparity check matrix H.

c=[mp]  Equation 1

Referring to Equation 1, the codeword c generated by the LDPC encoder100 may be divided into the data m and a parity bit p.

For example, the data m may correspond to a set of binary data [m_0,m_1, m_2, . . . , m_K−1]. That is, it may be understood that the lengthof the data m to be encoded is K.

For example, the parity bit p may correspond to a set of binary data[p_0, p_1, p_2, . . . p_N+2Zc-K−1]. That is, it may be understood thatthe length of the parity bit p is N+2Zc-K. In this case, N may be 50Zc(i.e., N=50Zc). Zc will be described later in detail with reference tothe drawings.

From the viewpoint of the LDPC encoder 100, the parity bit p forencoding the data m may be derived using the parity check matrix H.

Additionally, it may be assumed that, on a channel coding chain, initialdata of a transport block size (hereinafter, ‘TBS’) exceeding a presetthreshold size (i.e., Kcb, for example, 8448 bits) is received from ahigher layer.

In this case, the initial data may be divided into at least two datadepending on the length K of data (where K is a natural number) to beencoded. In other words, the length K of the data m may be understood asa code block size (CBS).

It may be understood that the parity check matrix H according to theembodiment of the present disclosure is applied when the CBS does notexceed a predetermined threshold value (e.g., 2040 bits).

Meanwhile, the LDPC decoder 400 may determine whether an error ispresent in the received codeword c based on the parity check matrix H.Whether an error is present in the received codeword c may be checked bythe LDPC decoder 400 based on Equation 2.

H·c ^(T)=0  Equation 2

As indicated in Equation 2, when multiplication of the parity checkmatrix H by a transposed matrix of the codeword c is ‘0’, the codeword creceived by the reception UE 20 may be determined not to include anerror value.

When the multiplication of the parity check matrix H by the transposedmatrix of the codeword c is not ‘0’, the codeword c received by thereception UE 20 may be determined to include an error value.

FIG. 2 is a diagram referenced to explain characteristics of a submatrixP.

Referring to FIGS. 1 and 2, the parity check matrix H may include aplurality of submatrices P_y (where y is an integer). In this case, itmay be appreciated that each submatrix is a matrix acquired by shiftingan identity matrix I having a size of Zc×Zc to the right by a specificvalue y.

Specifically, since the subscript y of a submatrix P_1 of FIG. 2 is ‘1’,the submatrix P_1 may be understood as a matrix obtained by shifting allelements included in the identity matrix I having a size of Zc×Zc to theright by one column. In this disclosure, Zc may be referred to as alifting value.

Although not shown in FIG. 2, since the subscript y of a submatrix P_0is ‘0’, the submatrix P_0 may be understood as the identity matrix Ihaving a size of Zc×Zc.

In addition, since the subscript y of a submatrix P_−1 is ‘−1’, thesubmatrix P_−1 may be understood as a zero matrix having a size ofZc×Zc.

FIG. 3 is a diagram illustrating a parity check matrix according to anembodiment of the present disclosure.

Referring to FIGS. 1 to 3, one submatrix P_am,n may be defined at everylocation m,n by each row m (where m is a natural number of 1 to 42) andeach column n (where n is a natural number of 1 to 52) of the paritycheck matrix H of FIG. 3.

The subscript (i.e., am,n) corresponding to the defined location m,n ofthe parity check matrix H of FIG. 3 is set to an integer value and maybe referred to as a shift index value.

Each submatrix P_am,n of FIG. 3 may be understood as a matrix obtainedby shifting the identity matrix I having a size of Zc×Zc to the right bythe shift index value am,n corresponding to the location (m,n). That is,an actual size of the parity check matrix H of FIG. 3 may be understoodas (m×Zc)×(n×Zc).

For example, the lifting value Zc according to the present embodimentmay be nay one of 15, 30, 60, 120, and 240. As another example, the liftvalue Zc may be any one of 3, 6, 12, 24, 48, 96, 192, and 384.

FIG. 4 is a diagram illustrating a characteristic matrix correspondingto a parity check matrix according to an embodiment of the presentdisclosure.

Referring to FIGS. 1 to 4, elements (i.e., a1,1 to am,n) according tothe location m,n determined by each row m (where m is a natural numberof 1 to 42) and each column n (where n is a natural number of 1 to 52)of the characteristic matrix Hc of FIG. 4 may be set as shift indexvalues at corresponding locations of the parity check matrix H of FIG.3.

That is, the parity check matrix H of FIG. 3 may be obtained by theelements according to the location m,n of the characteristic matrix Hcof FIG. 4 and the preset lifting value Zc.

The element am,n of the characteristic matrix Hc of FIG. 4 may bedefined as indicated below in Equation 3.

$\begin{matrix}{{am},{n = \left\{ \begin{matrix}{{Vm},n} & {{{if}\mspace{14mu} {Vm}},{m < 0}} \\{{{mod}\; \left( {{Vm},n,{Zc}} \right)},} & {otherwise}\end{matrix} \right.}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

The lifting value Zc of Equation 3 may be any one of 15, 30, 60, 120,and 240. As another example, the lifting value Zc may be any one of 3,6, 12, 24, 48, 96, 192, and 384.

In Equation 3, Vm,n may be an element of a corresponding location m,n ina base matrix (hereinafter ‘fib’) which will be described later.

For example, it may be assumed that the shift index value am,ncorresponding to the location m,n of the parity check matrix H, obtainedby Equation 3, is equal to or greater than ‘1’.

In this case, the submatrix P_am,n corresponding to the location m,n ofFIG. 3 may be understood as a matrix obtained by shifting all elementsincluded in the identity matrix I having a size of Zc×Zc (where Zc is anatural number) to the right by the shift index value (i.e., am,n)corresponding to the location (m,n) of FIG. 3.

As another example, it may be assumed that the shift index value am,ncorresponding to the location m,n of the parity check matrix H, obtainedby Equation 3, is ‘0’.

In this case, the submatrix P_am,n corresponding to the location m,n ofFIG. 3 may maintain the identity matrix I having a size of Zc×Zc (whereZc is a natural number).

As still another example, it may be assumed that the shift index valueam,n corresponding to the location m,n of the parity check matrix H,obtained by Equation 3, is ‘−1’.

In this case, the submatrix P_am,n corresponding to the location m,n ofFIG. 3 may be replaced with a zero matrix having a size of Zc×Zc.

FIG. 5 is a diagram illustrating the structure of a base matrix for aparity check matrix according to an embodiment of the presentdisclosure.

Referring to FIGS. 1 to 5, the parity check matrix H of FIG. 3 may begenerated based on the characteristic matrix Hc of FIG. 4 and thelifting value Zc. The characteristic matrix Hc of FIG. 4 may be acquiredthrough operation of Equation 3 based on the base matrix Hb of FIG. 5and the lifting value Zc.

Referring to FIGS. 1 to 5, the base matrix Hb of FIG. 3 according to thepresent embodiment may include 4 submatrices A, B, C, and D.

The size of the base matrix Hb according to the present embodiment maybe 42×52. A predetermined element Vm,n may be disposed at every locationm,n defined by each row m (where m is a natural number of 1 to 42) andeach column n (where n is a natural number of 1 to 52) of the basematrix Hb.

The matrix A of FIG. 5 may include a plurality of elements correspondingto 1st to 17th columns of the base matrix Hb in 1st to 7th rows of thebase matrix Hb. The matrix A will be described later in detail withreference to FIG. 6.

The matrix B of FIG. 5 may include elements corresponding to 18th to52nd columns of the base matrix Hb in the 1st to 7th rows of the basematrix Hb, which are all ‘-1’.

The matrix C of FIG. 5 may include a plurality of elements correspondingto the 1st to 17th columns of the base matrix Hb in 8th to 42nd rows ofthe base matrix Hb. The matrix C will be described later in detail withreference to FIGS. 7A and 7B.

The matrix D of FIG. 5 may include a plurality of elements correspondingto the 18th to 52nd columns of the base matrix Hb in the 8th to 42ndrows of the base matrix Hb. The matrix D will be described later indetail with reference to FIGS. 8A and 8B.

In addition, elements corresponding to a plurality of specificpredetermined columns of the base matrix Hb may be punctured. Forexample, elements corresponding to the 1st and 2nd columns of the basematrix Hb may be punctured.

Hereinafter, respective elements Vm,n of the matrices A, B, C, and Dincluded in the base matrix Hb will be described in detail withreference to subsequent drawings.

FIG. 6 illustrates a matrix A included in a base matrix according to anembodiment of the present disclosure.

Referring to FIGS. 1 to 6, elements Vm,n defined by the 1st row (m=1)and 1st to 17th columns (n=1, . . . , 17) of the matrix A belonging tothe base matrix Hb may be{145,131,71,21,−1,−1,23,−1,−1,112,1,0,−1,−1,−1,−1,−1}.

Elements Vm,n defined by the 2nd row (m=2) and the 1st to 17th columns(n=1, . . . , 17) of the matrix A belonging to the base matrix Hb may be{142,−1,−1,174,183,27,96,23,9,167,−1,0,0,−1,−1,−1,−1}.

Elements Vm,n defined by the 3rd row (m=3) and the 1st to 17th columns(n=1, . . . , 17) of the matrix A belonging to the base matrix Hb may be{74,31,−1,3,53,−1,−1,−1,155,−1,0,−1,0,0,−1,−1,−1}.

Elements Vm,n defined by the 4th row (m=4) and the 1st to 17th columns(n=1, . . . , 17) of the matrix A belonging to the base matrix Hb may be{4,239,171,−1,95,110,159,199,43,75,1,−1,−1,0,−1,−1,−1}.

Elements Vm,n defined by the 5th row (m=5) and the 1st to 17th columns(n=1, . . . , 17) of the matrix A belonging to the base matrix Hb may be{29,140,−1,−1,−1,−1,−1,−1,−1,−1,−1,180,−1,−1,0,−1,−1}.

Elements Vm,n defined by the 6th row (m=6) and the 1st to 17th columns(n=1, . . . , 17) of the matrix A belonging to the base matrix Hb may be{121,41,−1,−1,−1,169,−1,88,−1,−1,−1,207,−1,−1,−1,0,−1}.

Elements Vm,n defined by the 7th row (m=7) and the 1st to 17th columns(n=1, . . . , 17) of the matrix A belonging to the base matrix Hb may be{137,−1,−1,−1,−1,72,−1,172,−1,124,−1,56,−1,−1,−1,−1,0}.

Referring to FIG. 6, a set of columns corresponding to the 1st to 10thcolumns (n=1, . . . 10) of the matrix A may be referred to asinformation columns. A maximum value for information columns Kb of thebase matrix Hb according to the present embodiment may be ‘10’. That is,the number Kb of information columns of the base matrix Hb may bevariably defined according to a TBS B of initial data received from ahigher layer.

The number Kb of information columns may be associated with the length Kof input data (e.g., m in FIG. 1) to be encoded and the lifting value Zcas indicated in Equation 4.

According to the embodiment of FIG. 6, the lifting value Zc of Equation4 may be any one of 15, 30, 60, 120, and 240. In the present disclosure,the lifting value Zc may be a value commonly used in the base matrix Hb.

Zc=K/Kb  Equation 4

Referring to Equation 4, a maximum information bit value K of the inputdata (m in FIG. 1) which is encoded (or can be encoded) based on theparity check matrix according to the present disclosure may be 150, 300,600, 1200, or 2400.

In addition, unlike the embodiment of FIG. 6, the lifting value Zc maybe any one of 3, 6, 12, 24, 48, 96, 192, and 384. In this case, themaximum information bit value K of the input data (m in FIG. 1) which isencoded (or can be encoded) based on the parity check matrix may be 30,60, 120, 240, 480, 960, 1920, or 3840.

For reference, the 7×17 matrix A of FIG. 6 according to the presentembodiment may be as indicated in Table 1.

TABLE 1 145 131 71 21 −1 −1 23 −1 −1 112 1 0 −1 −1 −1 −1 −1 142 −1 −1174 183 27 96 23 9 167 −1 0 0 −1 −1 −1 −1 74 31 −1 3 53 −1 −1 −1 155 −10 −1 0 0 −1 −1 −1 −1 239 171 −1 95 110 159 199 43 75 1 −1 −1 0 −1 −1 −129 140 −1 −1 −1 −1 −1 −1 −1 −1 −1 180 −1 −1 0 −1 −1 121 41 −1 −1 −1 169−1 88 −1 −1 −1 207 −1 −1 −1 0 −1 137 −1 −1 −1 −1 72 −1 172 −1 124 −1 56−1 −1 −1 −1 0

FIGS. 7A and 7B illustrate a matrix C belonging to a base matrixaccording to an embodiment of the present disclosure.

Referring to FIGS. 1 to 6 and 7A, elements Vm,n corresponding to the 1stto 17th columns (n=1, . . . , 17) of the base matrix Hb in the 8th row(m=8) of the matrix C belonging to the base matrix Hb may be{−1,86,−1,−1,−1,186,−1,87,−1,−1,−1,172,−1,154,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 9th row (m=9) of the matrix C belonging tothe base matrix Hb may be{176,169,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,225,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 10th row (m=10) of the matrix C belongingto the base matrix Hb may be{4,167,−1,−1,−1,−1,−1,−1,238,−1,48,68,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 11th row (m=11) of the matrix C belongingto the base matrix Hb may be{38,217,−1,−1,−1,−1,208,232,−1,−1,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 12th row (m=12) of the matrix C belongingto the base matrix Hb may be{178,−1,−1,−1,−1,−1,−1,214,−1,168,−1,−1,−1,51,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 13th row (m=13) of the matrix C belongingto the base matrix Hb may be{4,124,−1,122,−1,−1,−1,−1,−1,−1,−1,72,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 14th row (m=14) of the matrix C belongingto the base matrix Hb may be{48,57,−1,−1,−1,−1,−1,−1,167,−1,−1,−1,−1,219,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 15th row (m=15) of the matrix C belongingto the base matrix Hb may be{−1,82,−1,−1,−1,−1,232,−1,−1,−1,−1,204,−1,162,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 16th row (m=16) of the matrix C belongingto the base matrix Hb may be{38,−1,−1,−1,−1,−1,−1,−1,−1,−1,217,157,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 17th row (m=17) of the matrix C belongingto the base matrix Hb may be{−1,170,−1,−1,−1,−1,−1,−1,−1,23,−1,175,202,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 18th row (m=18) of the matrix C belongingto the base matrix Hb may be{4,196,−1,−1,−1,173,−1,−1,−1,−1,−1,195,218,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 19th row (m=19) of the matrix C belongingto the base matrix Hb may be{128,−1,−1,−1,−1,−1,211,210,−1,−1,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 20th row (m=20) of the matrix C belongingto the base matrix Hb may be{39,84,−1,−1,−1,−1,−1,−1,−1,−1,88,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 21st row (m=21) of the matrix C belongingto the base matrix Hb may be{−1,117,−1,−1,227,−1,−1,−1,−1,−1,−1,6,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 22nd row (m=22) of the matrix C belongingto the base matrix Hb may be{238,−1,−1,−1,−1,−1,−1,−1,13,−1,−1,−1,−1,11,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 23rd row (m=23) of the matrix C belongingto the base matrix Hb may be{−1,195,44,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 24th row (m=10) of the matrix C belongingto the base matrix Hb may be{5,−1,−1,94,−1,111,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 25th row (m=25) of the matrix C belongingto the base matrix Hb may be{4,81,19,−1,−1,−1,−1,−1,−1,130,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 26th row (m=26) of the matrix C belongingto the base matrix Hb may be{66,−1,−1,−1,−1,95,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 27th row (m=27) of the matrix C belongingto the base matrix Hb may be{4,−1,146,−1,−1,−1,−1,66,−1,−1,−1,−1,190,86,−1,−1,−1}.

For reference, a part of the matrix C mentioned in FIG. 7A according tothe present embodiment may be as indicated in Table 2.

TABLE 2 −1 86 −1 −1 −1 186 −1 87 −1 −1 −1 172 −1 154 −1 −1 −1 176 169 −1−1 −1 −1 −1 −1 −1 −1 −1 −1 225 −1 −1 −1 −1 −1 167 −1 −1 −1 −1 −1 −1 238−1 48 68 −1 −1 −1 −1 −1 38 217 −1 −1 −1 −1 208 232 −1 −1 −1 −1 −1 −1 −1−1 −1 178 −1 −1 −1 −1 −1 −1 214 −1 168 −1 −1 −1 51 −1 −1 −1 −1 124 −1122 −1 −1 −1 −1 −1 −1 −1 72 −1 −1 −1 −1 −1 48 57 −1 −1 −1 −1 −1 −1 167−1 −1 −1 −1 219 −1 −1 −1 −1 82 −1 −1 −1 −1 232 −1 −1 −1 −1 204 −1 162 −1−1 −1 38 −1 −1 −1 −1 −1 −1 −1 −1 −1 217 157 −1 −1 −1 −1 −1 −1 170 −1 −1−1 −1 −1 −1 −1 23 −1 175 202 −1 −1 −1 −1 −1 196 −1 −1 −1 173 −1 −1 −1 −1−1 195 218 −1 −1 −1 −1 128 −1 −1 −1 −1 −1 211 210 −1 −1 −1 −1 −1 −1 −1−1 −1 39 84 −1 −1 −1 −1 −1 −1 −1 −1 88 −1 −1 −1 −1 −1 −1 −1 117 −1 −1227 −1 −1 −1 −1 −1 −1 6 −1 −1 −1 −1 −1 238 −1 −1 −1 −1 −1 −1 −1 13 −1 −1−1 −1 11 −1 −1 −1 −1 195 44 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 5−1 −1 94 −1 111 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 81 19 −1 −1 −1 −1 −1−1 130 −1 −1 −1 −1 −1 −1 −1 66 −1 −1 −1 −1 95 −1 −1 −1 −1 −1 −1 −1 −1 −1−1 −1 −1 −1 146 −1 −1 −1 −1 66 −1 −1 −1 −1 190 86 −1 −1 −1

Referring to FIGS. 1 to 6 and FIG. 7B, elements Vm,n corresponding tothe 1st to 17th columns (n=1, . . . , 17) of the base matrix Hb in the28th row (m=10) of the matrix C belonging to the base matrix fib may be{64,−1,−1,−1,−1,−1,181,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 29th row (m=29) of the matrix C belongingto the base matrix Hb may be{−1,7,144,−1,−1,16,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 30th row (m=30) of the matrix C belongingto the base matrix Hb may be{25,−1,−1,−1,57,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 31st row (m=31) of the matrix C belongingto the base matrix Hb may be{4,−1,37,−1,−1,139,−1,221,−1,17,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 32nd row (m=32) of the matrix C belongingto the base matrix Hb may be{4,201,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,46,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 33rd row (m=33) of the matrix C belongingto the base matrix Hb may be{179,−1,−1,−1,−1,14,−1,−1,−1,−1,−1,−1,116,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 34th row (m=34) of the matrix C belongingto the base matrix Hb may be{4,−1,46,−1,−1,−1,−1,2,−1,−1,106,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 35th row (m=35) of the matrix C belongingto the base matrix Hb may be{184,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,−1,135,141,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 36th row (m=36) of the matrix C belongingto the base matrix Hb may be{4,85,−1,−1,−1,225,−1,−1,−1,−1,−1,175,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 37th row (m=37) of the matrix C belongingto the base matrix Hb may be{178,−1,112,−1,−1,−1,−1,106,−1,−1,−1,−1,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 38th row (m=38) of the matrix C belongingto the base matrix Hb may be{4,−1,−1,−1,−1,−1,−1,−1,−1,−1,154,−1,−1,114,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 39th row (m=39) of the matrix C belongingto the base matrix Hb may be{4,42,−1,−1,−1,41,−1,−1,−1,−1,−1,105,−1,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 40th row (m=40) of the matrix C belongingto the base matrix Hb may be{167,−1,−1,−1,−1,−1,−1,45,−1,−1,−1,−1,189,−1,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 41st row (m=41) of the matrix C belongingto the base matrix Hb may be{4,−1,78,−1,−1,−1,−1,−1,−1,−1,67,−1,−1,180,−1,−1,−1}.

Elements Vm,n corresponding to the 1st to 17th columns (n=1, . . . , 17)of the base matrix Hb in the 42nd row (m=42) of the matrix C belongingto the base matrix Hb may be{4,53,−1,−1,−1,215,−1,−1,−1,−1,−1,230,−1,−1,−1,−1,−1}.

For reference, a part of the matrix C mentioned in FIG. 7B according tothe present embodiment may be as indicated in Table 3.

TABLE 3 64 −1 −1 −1 −1 −1 181 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 7 144 −1−1 16 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 25 −1 −1 −1 57 −1 −1 −1 −1 −1 −1−1 −1 −1 −1 −1 −1 −1 −1 37 −1 −1 139 −1 221 −1 17 −1 −1 −1 −1 −1 −1 −1−1 201 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 46 −1 −1 −1 179 −1 −1 −1 −1 14−1 −1 −1 −1 −1 −1 116 −1 −1 −1 −1 −1 −1 46 −1 −1 −1 −1 2 −1 −1 106 −1 −1−1 −1 −1 −1 184 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 135 141 −1 −1 −1 −1 85−1 −1 −1 225 −1 −1 −1 −1 −1 175 −1 −1 −1 −1 −1 178 −1 112 −1 −1 −1 −1106 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 −1 154 −1 −1114 −1 −1 −1 −1 42 −1 −1 −1 41 −1 −1 −1 −1 −1 105 −1 −1 −1 −1 −1 167 −1−1 −1 −1 −1 −1 45 −1 −1 −1 −1 189 −1 −1 −1 −1 −1 −1 78 −1 −1 −1 −1 −1 −1−1 67 −1 −1 180 −1 −1 −1 −1 53 −1 −1 −1 215 −1 −1 −1 −1 −1 230 −1 −1 −1−1 −1

FIGS. 8A and 8B illustrate a matrix D belonging to a base matrixaccording to an embodiment of the present disclosure.

Referring to FIGS. 1 to 8A, the matrix D belonging to the base matrix Hbmay include a plurality of elements corresponding to the 18th to 52ndcolumns (n=18, . . . , 52) of the base matrix Hb in the 8th to 25th rows(m=8, . . . , 25) of the base matrix Hb.

Referring to FIGS. 1 to 7 and 8B, the matrix D belonging to the basematrix Hb may include a plurality of elements corresponding to the 18thto 52nd columns (n=18, . . . , 52) of the base matrix Hb in the 26th to42nd rows (m=26, . . . , 42) of the base matrix Hb.

18 diagonal elements illustrated in FIG. 8A may be understood as aplurality of elements corresponding to a plurality of locations definedby a plurality of rows (m=8, . . . , 25) and a plurality of columns(n=18, . . . , 52) satisfying Equation 5 indicated below.

Similarly, 17 diagonal elements illustrated in FIG. 8B may be understoodas elements corresponding to locations defined by rows (m=26, . . . ,42) and columns (n=18, . . . , 52) satisfying Equation 5 indicatedbelow.

m+10−n  Equation 5

FIG. 9 is a flowchart illustrating a method of performing encoding basedon a parity check matrix of an LDPC code according to an embodiment ofthe present disclosure.

Referring to FIGS. 1 to 9, a UE according to this embodiment maygenerate the parity check matrix of the LDPC code in step S910.

The parity check matrix according to this embodiment may correspond to acharacteristic matrix. The characteristic matrix may include a maximumof 10 information columns for input data.

Each element of the characteristic matrix may correspond to a shiftindex value determined through a modulo operation between an element ofa location corresponding to the element of the characteristic matrix inthe base matrix and a lifting value. In addition, the base matrix may bea 42×52 matrix. As described above, the base matrix may be defined as aform as shown in FIG. 5.

In this disclosure, the lifting value may be associated with the lengthof the input data. In this disclosure, the lifting value may bedetermined as one of 15, 30, 60, 120, and 240.

The matrix A (i.e., A of FIG. 5) belonging to the base matrix Hb of thisdisclosure may include a plurality of elements corresponding to the 1stto 17th columns of the base matrix in the 1st to 7th rows of the basematrix. In this case, the plural elements of the matrix A (i.e., A ofFIG. 5) may correspond to the elements shown in FIG. 6.

The matrix B (i.e., B of FIG. 5) belonging to the base matrix Hb of thisdisclosure may include a plurality of elements corresponding to the 18thto 52nd columns of the base matrix in the 1st to 7th rows of the basematrix.

Specifically, all of the elements corresponding to the 18th to 52ndcolumns of the base matrix in the 1st row of the base matrix Hb may be‘−1’. All of the elements corresponding to the 18th to 52nd columns ofthe base matrix in the second row of the base matrix may be ‘−1’. All ofthe elements corresponding to the 18th to 52nd columns of the basematrix in the 3rd row of the base matrix may be ‘−1’. All of theelements corresponding to the 18th to 52nd columns of the base matrix inthe 4th row of the base matrix may be ‘−1’.

All of the elements corresponding to the 18th to 52nd columns of thebase matrix in the 5th row of the base matrix may be ‘−1’. All of theelements corresponding to the 18th to 52nd columns of the base matrix inthe 6th row of the base matrix may be ‘−1’. All of the elementscorresponding to the 18th to 52nd columns of the base matrix in the 7throw of the base matrix may be ‘−1’.

The matrix C (i.e., C of FIG. 5) belonging to the base matrix Hb of thisdisclosure may include a plurality of elements corresponding to the 1stto 17th columns of the base matrix in the 8th to 42nd rows of the basematrix. The plural elements of the matrix C (i.e., C of FIG. 5) maycorrespond to the elements described in FIGS. 7A and 7B.

In the matrix D (i.e., D of FIG. 5) belonging to the base matrix Hb ofthis disclosure, plural elements corresponding to the 18th to 52ndcolumns of the base matrix in the 8th to 42nd rows of the base matrixmay correspond to all elements of a 35×35 identity matrix.

Notably, the aforementioned modulo operation of Equation 3 may beperformed when an element corresponding to the characteristic matrix inthe base matrix is an integer equal to or greater than 0.

When a corresponding element in the base matrix is −1, the modulooperation of Equation 3 is not performed and −1 may be determined as anelement of the characteristic matrix. In this disclosure, when acorresponding element in the base matrix Hb is ‘−1’, the correspondingelement may correspond to a zero matrix.

For example, when the shift index value is ‘0’ or a natural number equalto or greater than ‘1’, each element of the characteristic matrix maycorrespond to a Zc×Zc identity matrix. All elements of the identitymatrix may be shifted to the right according to the shift index value.

In step S920, the UE according to the present embodiment may encode theinput data using the parity check matrix.

If the present embodiment described with reference to FIGS. 1 to 9 isapplied, when the shift index value of the characteristic matrix of FIG.4 is changed according to the length of information bits based on asingle base matrix of FIG. 5, the parity check matrix (e.g., FIG. 3) ofan LDPC code having high reliability in terms of latency can beobtained.

FIG. 10 is a flowchart illustrating a method of performing a decodingprocedure for a transport block based on any one of parity checkmatrices of two types according to another embodiment of the presentdisclosure.

According to the embodiment of FIG. 10, a first parity check matrix maybe defined based on a base matrix having a size of 46×68. For example,the first parity check matrix may have a first maximum information bitvalue (e.g., 8448).

According to the embodiment of FIG. 10, a second parity check matrix maybe defined based on a base matrix having a size of 42×52. For example,the second parity check matrix may have a second maximum information bitvalue (e.g., 3840). In this case, it may be understood that the secondparity check matrix based on the base matrix having a size of 42×52 isbased on the above description given with reference to FIGS. 1 to 9.

In the present disclosure, the first parity check matrix or the secondparity check matrix may be determined according to a predetermined ruleduring initial transmission of a transport block (TB) having a code rateR and retransmission of the same TB.

In step S1010, the UE may determine whether the code rate R derived froma modulation and coding scheme (MCS) index according to receiveddownlink control information (DCI) is equal to or less than apredetermined value (e.g., 0.25). If the code rate R derived from theMCS index is equal to or less than the predetermined value, step S1020may be performed.

In step S1020, the UE may decode a code block (CB) based on the secondparity check matrix based on the base matrix having a size of 42×52.

If it is determined that the code rate R derived from the MCS indexexceeds the predetermined value in step S1010, step S1030 may beperformed.

In step S1030, the UE may decode the CB based on the first parity checkmatrix based on the base matrix having a size of 46×68.

Which of the first parity check matrix and the second parity checkmatrix is used as a parity check matrix for an encoding or decodingprocedure by the UE may differ according to a code rate, a TBS, a CBsize, a service type provided to the UE, or a type of a partial band onwhich the UE receives a signal.

FIG. 11 is a flowchart illustrating a method of performing CBsegmentation based on a parity check matrix of an LDPC accord to anotherembodiment of the present disclosure.

According to the embodiment of FIG. 11, a first parity check matrix maybe defined based on a base matrix having a size of 46×68. The firstparity check matrix may have a first maximum information bit value(e.g., 8448). For example, the first maximum information bit value(e.g., 8448) may represent the length of input data capable of beingencoded based on the first parity check matrix.

According to the embodiment of FIG. 11, a second parity check matrix maybe defined based on a base matrix having a size of 42×52. The secondparity check matrix may have a second maximum information bit value(e.g., 3840). For example, the second maximum information bit value(e.g., 3840) may represent the length of input data capable of beingencoded based on the second parity check matrix.

In this case, the second parity check matrix based on the base matrixhaving a size of 42×52 may be understood based on the above descriptiongiven with reference to FIGS. 1 to 9.

Referring to FIGS. 10 and 11, in step S1110, a UE may determine, basedon a code rate for a TB, any one of the first parity check matrix havingthe first maximum information bit value and the second parity checkmatrix having the second maximum information bit value as a parity checkmatrix for encoding the TB.

To simplify and clarify a description of FIG. 10, it may be assumed thatthe code rate for the TB is equal to or less than a predetermined value(e.g., 0.25). According to the above assumption, the UE may determinethe second parity check matrix as the parity check matrix for encodingthe TB.

If the second parity check matrix is determined as the parity checkmatrix, the procedure proceeds to step S1120. Although not shown in FIG.11, if the second parity check matrix is determined as the parity checkmatrix, the UE may add a second cyclic redundancy check (CRC) of 16 bitsto the TB.

If the first parity check matrix is determined as the parity checkmatrix, the procedure may be ended. Although not shown in FIG. 11, ifthe first parity check matrix is determined as the parity check matrix,the UE may add a first CRC of 24 bits to the TB.

In S1120, the UE may perform CB segmentation for the TB based on thesecond maximum information bit value of the second parity check matrix.For example, if CB segmentation is performed, at least two CBs may beobtained from the TB. Code block segmentation of step S1120 may beperformed based on the second maximum information bit value even if thelength of the TB exceeds the first maximum information bit value.

For example, the UE may identify whether the first parity check matrixis applied or the second parity check matrix is applied according to apre-agreed rule between the UE and a base station. Next, the UE maydetermine whether a CRC applied to a CB and/or a TB is a first type CRCor a second type CRC, based on the identified result.

In the above example, if the code rate is derived during uplinktransmission, resource elements (REs) occupied by multiplexedinformation such as a channel quality indicator (CQI) may be excludedfrom a calculation process of the code rate. In addition, a code rateapplied to each CB may be calculated in a state in which REs occupied bypunctured information such as ACK/NACK are considered.

FIG. 12 is a flowchart illustrating a method of performing a decodingprocedure based on a parity check matrix according to another embodimentof the present disclosure.

According to the embodiment of FIG. 12, a first parity check matrixbased on a base matrix having a size of 46×68 may be defined. Forexample, the first parity check matrix may have a first maximuminformation bit value (e.g., 8448).

According to the embodiment of FIG. 12, a second check matrix based on abase matrix having a size of 42×52 may be defined. For example, thesecond parity check matrix may have a second maximum information bitvalue (e.g., 3840). In this case, it may be understood that the secondparity check matrix based on the base matrix having a size of 42×52 isbased on the above description given with reference to FIGS. 1 to 9.

Referring to FIGS. 10 to 12, in step S1210, the UE may determine whetherDCI indicates retransmission scheduling. If the DCI does not indicateretransmission scheduling, the procedure may be ended. If the DCIindicates retransmission scheduling (i.e., when a new data indicator isnot toggled or the new data indicator is set to ‘0’), the procedureproceeds to step S1220.

In step S1220, the UE may perform the decoding procedure based on theparity check matrix which has been applied during initial reception of aTB. In this case, the parity check matrix may be the first parity checkmatrix or the second parity check matrix.

Specifically, the UE may perform the decoding procedure based on aparity check matrix corresponding to the case in which a TB mapped to aretransmission process ID is first received (i.e., the case in which thenew data indicator is toggled or the new data indicator is set to ‘1’).

1-20. (canceled)
 21. A method of encoding information, by a transmittingdevice using a parity check matrix of a low-density parity-check code,for transmission over a communication channel, the method comprising:determining, by the transmitting device, the parity check matrix ofdimensions at least 7 rows and 172 columns comprising 7 rows and 17columns of Z×Z-sized submatrices that are indexed by submatrix row indexm (where 0≤m≤6) and submatrix column index n (where 0≤n≤16), wherein Zis a non-zero integer, and wherein: for submatrix row index m=0 and forsubmatrix column indices n={0,1,2,3,6,9,10,11}, each submatrix atsubmatrix index Own) is equal to a circularly column-shifted identitymatrix of size Z×Z that is circularly column-shifted by a shift indexvalue α_(m,n) that is defined by taking a modulo operation that involvesa respective value among {145,131,71,21,23,112,1,0}, for submatrix rowindex m=1 and for submatrix column indices n={0,3,4,5,6,7,8,9,11,12},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among{142,174,183,27,96,23,9,167,0,0}, for submatrix row index m=2 and forsubmatrix column indices n={0,1,3,4,8,10,12,13}, each submatrix atsubmatrix index (m,n) is equal to a circularly column-shifted identitymatrix of size Z×Z that is circularly column-shifted by a shift indexvalue α_(m,n) that is defined by taking a modulo operation that involvesa respective value among {74,31,3,53,155,0,0,0}, for submatrix row indexm=3 and for submatrix column indices n={1,2,4,5,6,7,8,9,10,15}, eachsubmatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among{259,171,95,110,159,199,43,75,1,0}, for submatrix row index m=4 and forsubmatrix column indices n={0,1,11,14}, each submatrix at submatrixindex (m,n) is equal to a circularly column-shifted identity matrix ofsize Z×Z that is circularly column-shifted by a shift index valueα_(m,n) that is defined by taking a modulo operation that involves arespective value among {29,140,180,0}, for submatrix row index m=5 andfor submatrix column indices n={0,1,5,7,11,15}, each submatrix atsubmatrix index (m,n) is equal to a circularly column-shifted identitymatrix of size Z×Z that is circularly column-shifted by a shift indexvalue α_(m,n) that is defined by taking a modulo operation that involvesa respective value among {121,41,169,88,207,0}, and for submatrix rowindex m=6 and for submatrix column indices n={0,5,7,9,11,16}, eachsubmatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value that is defined by taking a modulooperation that involves a respective value among {157,72,172,124,56,0},generating encoded data, by the transmitting device, based on encodingthe information with the determined parity check matrix; andtransmitting, by a transceiver of the transmitting device, the encodeddata over the communication channel.
 22. The method according to claim21, wherein in each of the submatrix row indices m=0, . . . , 6, theshift index value α_(m,n) is defined by taking the modulo operation thatfurther involves Z.
 23. The method according to claim 21, wherein forsubmatrix row index m=0 and for submatrix column indices other thann={0,1,2,3,6,9,10,11}, each submatrix at submatrix index (m,n) is equalto an all-zero matrix of size Z×Z, for submatrix row index m=1 and forsubmatrix column indices other than n={0,3,4,5,6,7,0,9,11,12}, eachsubmatrix at submatrix index (m,n) is equal to an all-zero matrix ofsize Z×Z, for submatrix row index m=Z and for submatrix column indicesother than n={0,1,3,4,8,10,12,13}, each submatrix at submatrix index(m,n) is equal to an all-zero matrix of size Z×Z, for submatrix rowindex m=3 and for submatrix column indices other thann={1,2,4,5,6,7,8,9,10,13}, each submatrix at submatrix index (m,n) isequal to an all-zero matrix of size Z×Z, for submatrix row index m=4 andfor submatrix column indices other than n={0,1,11,14}, each submatrix atsubmatrix index (m,n) is equal to an all-zero matrix of size Z×Z, forsubmatrix row index m=5 and for submatrix column indices other thann={0,1,5,7,11,15}, each submatrix at submatrix index (m,n) is equal toan all-zero matrix of size Z×Z, and for submatrix row index m=6 and forsubmatrix column indices other than n={0,5,7,9,11,16}, each submatrix atsubmatrix index (m,n) is equal to an all-zero matrix of size Z×Z. 24.The method according to claim 21, wherein the parity check matrix hasdimensions of 42Z rows comprising 42 rows of Z×Z-sized submatrices thatare indexed by submatrix row index m (where 0≤m≤41), and wherein: forsubmatrix row index m=7 and for submatrix column indicesn={1,5,7,11,13}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among{86,186,87,172,154}, for submatrix row index m=8 and for submatrixcolumn indices n={0,1,12}, each submatrix at submatrix index (m,n) isequal to a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{176,169,225}, for submatrix row index m=9 and for submatrix columnindices n={1,8,10,11}, each submatrix at submatrix index (m,n) is equalto a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{167,288,48,68}, for submatrix row index m=10 and for submatrix columnindices n={0,1,6,7}, each submatrix at submatrix index (m,n) is equal toa circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{86,217,208,232}, for submatrix row index m=11 and for submatrix columnindices n={0,7,9,13}, each submatrix at submatrix index (m,n) is equalto a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index α_(m,n) value that is definedby taking a modulo operation that involves a respective value among{176,214,168,51}, for submatrix row index m=12 and for submatrix columnindices n={1,8,11}, each submatrix at submatrix index (m,n) is equal toa circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{124,122,72}, for submatrix row index m=13 and for submatrix columnindices n={1,6,11,13}, each submatrix at submatrix index is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index α_(m,n) value that is defined by takinga modulo operation that involves a respective value among{48,57,167,219}, for submatrix row index m=14 and for submatrix columnindices n={1,6,11,15}, each submatrix at submatrix index (m,n) is equalto a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{82,232,204,162}, for submatrix row index m=15 and for submatrix columnindices n={0,10,11}, each submatrix at submatrix index (m,n) is equal toa circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{38,217,157}, for submatrix row index m=16 and for submatrix columnindices n={1,9,11,12}, each submatrix at submatrix index (m,n) is equalto a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{170,23,175,202}, for submatrix row index to m=17 and for submatrixcolumn indices n={1,5,11,12}, each submatrix at submatrix index (m,n) isequal to a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{196,175,195,218}, for submatrix row index m=18 and for submatrix columnindices n={0,6,7}, each submatrix at submatrix index (m,n): is equal toa circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{128,211,210}, for submatrix row index m=19 and for submatrix columnindices n={0,1,10}, each submatrix at submatrix index (m,n) is equal toa circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{39,84,88}, for submatrix row index m=20 and for submatrix columnindices n={1,4,11}, each submatrix at submatrix index (m,n) is equal toa circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{117,327,6}, for submatrix row index m=21 and for submatrix columnindices n={0,6,13}, each submatrix at submatrix index (m,n) is equal toa circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{238,13,11}, for submatrix row index m=22 and for submatrix columnindices n={1,2}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {195,44}, forsubmatrix row index m=23 and for submatrix column indices n={0,3,5},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {5,94,111},for submatrix row index m=24 and for submatrix column indices n={1,2,9},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {61,19,130},for submatrix row index m=25 and for submatrix column indices n={0,5},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {66,95}, forsubmatrix row index m=26 and for submatrix column indices n={3,8,13,14},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among{146,66,190,86}, for submatrix row index m=27 and for submatrix columnindices n={0,6}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {64,181}, forsubmatrix row index m=28 and for submatrix column indices n={1,2,5},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {7,144,16},for submatrix row index m=29 and for submatrix column indices n={0,4},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {25,57}, forsubmatrix row index m=30 and for submatrix column indices m={2,5,7,9},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among{37,139,221,17}, for submatrix row index m=31 and for submatrix columnindices n={1,19}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {201,46}, forsubmatrix row index m=32 and for submatrix column indices n={0,5,12},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {179,14,116},for submatrix row index m=33 and for submatrix column indicesn={2,7,10}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {46,2,106},for submatrix row index m=34 and for submatrix column indicesn={0,12,15}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {184,135,141},for submatrix row index m=35 and for submatrix column indicesn={1,5,11}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {85,225,175},for submatrix row index m=36 and for submatrix column indices n={0,2,7},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {176,112,106},for submatrix row index m=37 and for submatrix column indices n={10,13},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {154,114}, forsubmatrix row index m=38 and for submatrix column indices n={1,5,11},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {42,41,105},for submatrix row index m=39 and for submatrix column indicesn={0,7,12}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {167,45,189},for submatrix row index m=40 and for submatrix column indicesn={2,10,13}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {70,67,180},and for submatrix row index m=41 and for submatrix column indicesn={1,5,11}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {53,215,230}.25. The method according to claim 24, wherein in each of the submatrixrow indices m=7, . . . 41, the shift index value α_(m,n) is defined bytaking the modulo operation that further involves Z.
 26. The methodaccording to claim 21, wherein the parity check matrix has dimensions ofat least 42Z rows and 52Z columns comprising 42 rows and 52 columns ofZ×Z-sized submatrices that are indexed by submatrix row index m (where0≤m≤41) and submatrix column index n (where 0≤n≤51), wherein forsubmatrix row indices m=7, . . . , 41 and submatrix column indices n=17,. . . , 51: each submatrix along the 35 diagonal elements at submatrixindex (m,n+10) is an un-shifted identity matrix of size Z×Z, and eachsubmatrix except for those along the 35 diagonal elements is an all-zeromatrix of size Z×Z.
 27. The method according to claim 21, whereingenerating the encoded data, by the transmitting device, based onencoding the information with the determined parity check matrixcomprises: generating, based on the information and the parity checkmatrix, a plurality of parity bits {right arrow over (p)} that satisfy:H·({right arrow over (x)}{right arrow over (y)})^(T)=0, where H is theparity check matrix, and {right arrow over (x)} is the information. 28.The method according to claim 21, wherein each circularly column-shiftedidentity matrix of size Z×Z that is circularly column-shifted by theshift index value α_(m,n) is circularly column-shifted to the right. 29.The method according to claim 21, wherein the Z of each submatrix isrelated to a size of the information that is encoded by the transmittingdevice.
 30. The method according to claim 29, wherein the Z represents alifting value that is any one of 15, 30, 60, 120, or 240, and whereinthe size of the information is 10 times Z.
 31. The method according toclaim 21, further comprising: determining a base matrix of size at least7×17 in which an element at location of the base matrix indicateswhether the submatrix at submatrix index (m,n) is equal to thecircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by the shift index value α_(m,n).
 32. The methodaccording to claim 21, further comprising: determining, by thetransmitting device, a modulation and coding scheme (MCS) indexaccording to downlink control information received by the transmittingdevice; deriving, by the transmitting device and from the MCS index, acode rate; determining, by the transmitting device, that the code ratedoes not satisfy a threshold criterion; and based on a determinationthat the code rate does not satisfy the threshold criterion, determiningthe parity check matrix of dimensions at least 7Z rows and 17Z columnsand performing encoding on the information using the parity check matrixto generate the encoded data.
 33. A transmitting device configured toencode, based on a parity check matrix of a low-density parity-checkcode, information for transmission over a communication channel, thetransmitting device comprising: at least one processor; and at least onecomputer memory operably connectable to the at least one processor andstoring instructions that, when executed, cause the at least oneprocessor to perform operations comprising: determining the parity checkmatrix of dimensions at least 7Z rows and 17Z columns comprising 7 rowsand 17 columns of Z×Z-sized submatrices that are indexed by submatrixrow index m (where 0≤m≤6) and submatrix column index n (where 0≤n≤16),wherein Z is a non-zero integer, and wherein: for submatrix row indexm=0 and for submatrix column indices n={0,1,2,3,6,9,10,11}, eachsubmatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among{145,131,71,21,25,112,1,0}, for submatrix row index m=1 and forsubmatrix column indices n={0,3,4,5,6,7,0,9,11,12}, each submatrix atsubmatrix index (m,n) is equal to a circularly column-shifted identitymatrix of size Z×Z that is circularly column-shifted by a shift indexvalue α_(m,n) that is defined by taking a modulo operation that involvesa respective value among {142,174,183,27,96,23,9,167,0,0}, for submatrixrow index m=2 and for submatrix column indices n={0,1,3,4,8,10,12,13},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among{74,31,3,53,155,0,0,0}, for submatrix row index in m=3 and for submatrixcolumn indices n={1,2,4,5,6,7,8,9,10,13}, each submatrix at submatrixindex (m,n) is equal to a circularly column-shifted identity matrix ofsize Z×Z that is circularly column-shifted by a shift index valueα_(m,n) that is defined by taking a modulo operation that involves arespective value among {259,171,95,110,159,199,43,75,1,0}, for submatrixrow index m=4 and for submatrix column indices n={0,1,11,14}, eachsubmatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among{29,140,100,0}, for submatrix row index m=5 and for submatrix columnindices n={0,1,5,7,11,15}, each submatrix at submatrix index (m,n) isequal to a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{121,41,169,88,207,0}, and for submatrix row index m=6 and for submatrixcolumn indices n={0,5,7,9,11,16}, each submatrix at submatrix index(m,n) is equal to a circularly column-shifted identity matrix of sizeZ×Z that is circularly column-shifted by a shift index value α_(m,n)that is defined by taking a modulo operation that involves a respectivevalue among {137,72,172,124,56,0}, generating encoded data based onencoding the information with the determined parity, check matrix; andtransmitting the encoded data.
 34. The transmitting device according toclaim 33, wherein in each of the submatrix row indices m=0, . . . , 6,the shift index value α_(m,n) is defined by taking the modulo operationthat further involves Z.
 35. The transmitting device according to claim33, wherein for submatrix row index m=0 and for submatrix column indicesother than n={0,1,2,3,6,9,10,11}, each submatrix at submatrix index(m,n) is equal to an all-zero matrix of size Z×Z, for submatrix rowindex m=1 and for submatrix column indices other thann={0,3,4,5,6,7,8,9,11,12}, each submatrix at submatrix index (m,n) isequal to an all-zero matrix of size Z×Z, for submatrix row index m=2 andfor submatrix column indices other than n={0,1,3,4,8,10,12,13}, eachsubmatrix at submatrix index (m,n) is equal to an all-zero matrix ofsize Z×Z, for submatrix row index m=3 and for submatrix column indicesother than n={1,2,4,5,6,7,8,9,10,13}, each submatrix at submatrix index(m,n) is equal to an all-zero matrix of size Z×Z, for submatrix rowindex m=4 and for submatrix column indices other than n={0,1,11,14},each submatrix at submatrix index (m,n) is equal to an all-zero matrixof size Z×Z, for submatrix row index m=5 and for submatrix columnindices other than n={0,1,5,7,11,15}, each submatrix at submatrix index(m,n) is equal to an all-zero matrix of size Z×Z, and for submatrix rowindex m=6 and for submatrix column indices other than n={0,5,7,9,11,16},each submatrix at submatrix index (m,n) is equal to an all-zero matrixof size Z×Z.
 36. The transmitting device according to claim 33, whereinthe parity check matrix has dimensions of 42Z rows comprising 42 rows ofZ×Z-sized submatrices that are indexed by submatrix row index m (where0≤m≤41), and wherein: for submatrix row index m=7 and for submatrixcolumn indices n={1,5,7,11,13}, each submatrix at submatrix index (m,n)is equal to a circularly column-shifted identity matrix of size Z×Z thatis circularly column-shifted by a shift index value α_(m,n) that isdefined by taking a modulo operation that involves a respective valueamong {86,186,87,172,154}, for submatrix row index m=8 and for submatrixcolumn indices n={0,1,12}, each submatrix at submatrix index (m,n) isequal to a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{176,169,225}, for submatrix row index m=9 and for submatrix columnindices n={1,8,10,11}, each submatrix at submatrix index (m,n) is equalto a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{167,236,46,68}, for submatrix row index m=10 and for submatrix columnindices n={0,1,6,7}, each submatrix at submatrix index (m,n) is equal toa circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{36,217,208,232}, for submatrix row index m=11 and for submatrix columnindices n={0,7,9,13}, each submatrix at submatrix index (m,n) is equalto a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{178,214,168,51}, for submatrix row index m=12 and for submatrix columnindices n={1,3,11}, each submatrix at submatrix index (m,n) is equal toa circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{124,122,72}, for submatrix row index m=13 and for submatrix columnindices n={0,1,8,13}, each submatrix at submatrix index (m,n) is equalto a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{48,57,167,219}, for submatrix row index m=14 and for submatrix columnindices n={1,6,11,13}, each submatrix at submatrix index (m,n) is equalto a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{82,282,204,162}, for submatrix row index m=15 and for submatrix columnindices n={0,10,11}, each submatrix at submatrix index (m,n) is equal toa circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{38,217,157}, for submatrix row index m=16 and for submatrix columnindices n={1,9,11,12}, each submatrix at submatrix index (m,n) is equalto a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{170,23,175,202}, for submatrix row index m=17 and for submatrix columnindices n={1,5,11,12}, each submatrix at submatrix index (m,n) is equalto a circularly column-shifted identity matrix of size Z×Z that iscircularly column-shifted by a shift index value α_(m,n) that is definedby taking a modulo operation that involves a respective value among{196,173,195,218}, for submatrix row index m=10 and for submatrix columnindices n={0,6,7}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {128,211,210},for submatrix row index m=19 and for submatrix column indicesn={0,1,10}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {39,84,88},for submatrix row index m=20 and for submatrix column indicesn={1,4,11}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {238,13,11},for submatrix row index m=21 and for submatrix column indicesn={0,8,18}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {238,13,11},for submatrix row index m=22 and for submatrix column indices n={1,2},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {195,44}, forsubmatrix row index m=23 and for submatrix column indices n={0,3,5},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {5,94,111},for submatrix row index m=24′ and for submatrix column indices n={0,5},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {81,19,130},for submatrix row index m=25 and for submatrix column indices n={0,5},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {66,95}, forsubmatrix row index m=26 and for submatrix column indices n={3,8,13,14},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among{146,66,190,86}, for submatrix row index m=27 and for submatrix columnindices n={0,6}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {64,181}, forsubmatrix row index m=28 and for submatrix column indices n={1,2,3},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n), that is defined by takinga modulo operation that involves a respective value among {7,144,16},for submatrix row index m=29 and for submatrix column indices n={0,4},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {25,37}, forsubmatrix row index m=30 and for submatrix column indices n={2,5,7,9},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among{37,139,221,17}, for submatrix row index m=31 and for submatrix columnindices n={1,13}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {201,46}, forsubmatrix row index m=32 and for submatrix column indices n={0,5,12},each submatrix at submatrix index) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {179,14,116},for submatrix row index m=33 and for submatrix column indicesn={3,7,10}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {46,2,106},for submatrix row index m=34 and for submatrix column indicesn={0,12,13}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {184,135,141},for submatrix row index m=35 and for submatrix column indicesn={1,5,11}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {85,225,175},for submatrix row index m=36 and for submatrix column indices n={0,2,7},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {178,112,106},for submatrix row index m=37 and for submatrix column indices n={10,12},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {154,114}, forsubmatrix row index m=30 and for submatrix column indices n={1,5,11},each submatrix at submatrix index (m,n) is equal to a circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {42,41,105},for submatrix row index m=59 and for submatrix column indicesn={0,7,12}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {167,45,189},for submatrix row index m=40 and for submatrix column indicesn={2,10,15}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {78,67,100},and for submatrix row index m=41 and for submatrix column indicesn={1,5,11}, each submatrix at submatrix index (m,n) is equal to acircularly column-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by a shift index value α_(m,n) that is defined by takinga modulo operation that involves a respective value among {53,215,230}.37. The transmitting device according to claim 33, wherein the paritycheck matrix has dimensions of at least 42Z rows and 52Z columnscomprising 42 rows and 52 columns of Z×Z-sized submatrices that areindexed by submatrix row index m (where 0≤m≤41) and submatrix columnindex n (where 0≤n≤51), wherein for submatrix row indices m=7, . . . ,41 and submatrix column indices n=17, . . . , 51: each submatrix alongthe 35 diagonal elements at submatrix index (m,n+10) is an un-shiftedidentity matrix of size A E, and each submatrix except for those alongthe 35 diagonal elements is an all-zero matrix of size Z×Z.
 38. Thetransmitting device according to claim 33, wherein each circularlycolumn-shifted identity matrix of size Z×Z that is circularlycolumn-shifted by the shift index value α_(m,n) is circularlycolumn-shifted to the right.
 39. The transmitting device according toclaim 33, wherein the Z of each submatrix is related to a size of theinformation that is encoded by the transmitting device.
 40. Thetransmitting device according to claim 39, wherein the Z represents alifting value that is any one of 15, 30, 60, 120, or 240, and whereinthe size of the information is 10 times Z.